Plasma etching is frequently used in semiconductor fabrication. In plasma etching, ions are accelerated by an electric field to etch exposed surfaces on a substrate. Broadband sampling is used to monitor the RF Metrology used plasma process chamber. During sampling, aliasing can occur when a sample rate of an analog/digital converter (ADC) is less than half the frequency of a sampled signal. This causes frequencies that exceed half the sampling rate of the analog/digital converter to fold over in the digital frequency domain and appear as lower or aliased frequencies. FIG. 1 depicts aliased frequency bands in a radio frequency (RF) spectrum of a dual frequency system. The dual frequency system includes a high (such as 25.6 MHz) and a low (such as 2 MHz) frequency RF source. The low frequency RF source (F1) is represented by a fundamental harmonic H1A and its associated harmonics H2A through H5A. For illustrative purposes only, each of the associated harmonics have peaks that incrementally descend after H1A. The high frequency RF source (F2) is represented by the fundamental harmonic H1B and its associated harmonics H2B through H5B. Harmonics H2B through H5B do not proportionally decrease in frequency as compared to the harmonics for the lower frequency RF source, H1B. This disproportionate decrease in frequency can be generally referred to as aliasing.
Signal distortions such as intermodulation distortion (IMD) corrupt aliased frequencies, thereby creating in-band interference. IMD occurs when two or more signals pass through a non-linear system. Energy contained in the input signal of a non-linear system is transformed at its output. The output includes a set of frequency components at the original frequencies along with additional components at new frequencies that were not contained in the input signal.
There are at least three scenarios of in-band interference that may occur during broadband sampling for monitoring of a plasma process. FIGS. 2A-2B depict a first scenario in which the IMD around a fundamental frequency bandwidth F2 coincides with a spectrally folded bandwidth (BW) of interest. FIG. 2A is a block diagram of five bandwidth regions 110, 120, 130, 140, 150 in which signal distortion has not yet occurred with respect to the bandwidth of F2. The bandwidths for the first region 110, the second region 120, third region 130, fourth region 140, and fifth region 150 depend upon the bandwidth of an unaliased frequency F2. These bandwidth regions can be determined using the equation associated with the arrows defining the boundaries for each region shown in FIG. 2A.
FIG. 2B is a block diagram of IMD interference regions 160, 170 that occur around the aliased fundamental frequency nF2 bandwidth, where “n” is an integer constant. As F2 changes, nF2 and the IMD products correspondingly change. Due to the ADC sample rate, the IMD products and nF2 can co-exist in the digital domain with F2 bandwidth, thereby causing an interference or spurious frequencies. Spurious frequencies are unwanted and non-harmonically related signals. The bandwidth regions can be determined using the equations associated with the arrows defining the boundaries for each region shown in FIG. 2B.
FIGS. 3A-3B depict a second scenario of band interference in which higher order IMD regions occur. In this example, the fringes of the spectrally folded bandwidth of interest are adjacent to, but do not crossover or coincide. FIG. 3A depicts a block diagram of IMD interference regions 160,170 that occur around the aliased fundamental frequency nF2 bandwidth and overlap mF2. When overlapping mF2, there is a probability that the IMD interference regions 160, 170 may coincide with the bandwidth of interest. FIG. 3B is a block diagram of IMD interference regions that occur around the aliased fundamental frequency mF2 bandwidth, where “m” is an integer constant. As F2 changes, mF2 and the IMD products correspondingly change. The bandwidth regions can be determined using the equations associated with the arrows defining the boundaries for each region shown in FIG. 2B. Similar to regions 160 and 170, regions 180 and 190 can overlap, in this example, mF2. When overlapping mF2, there is a probability that at least one of the IMD regions 180, 190 may coincide with the bandwidth of interest.
FIG. 4 depicts a third scenario of band interference that involves IMD and an aliased bandwidth interference region. In this example, bandwidth region 200 lies adjacent to bandwidth region 210. The bandwidth regions can be determined using the equations associated with the arrows defining the boundaries for each region shown in FIG. 4. Half the sampling frequency (Fs/2), commonly referred to as the Nyquist frequency, occurs in bandwidth region 200 or 210. Specifically, the Nyquist frequency occurs at a region associated with the formula nF2−2F1. The nF2 frequency component then spectrally folds and coincides with the region of nF2−2F1.
Conventional systems such as is disclosed in U.S. Pat. No. 6,522,121, issued Feb. 18, 2003, the disclosure of which is incorporated by reference in its entirety herein, describes a configuration of anti-aliasing filters and sample rate that generally prevents signal distortions. For example, a multiple digital filter with a narrow passband is typically used to address this problem. However, conventional methods fail to detect and connect or to prevent alleviate distorted signals that occur when the IMD or spurious frequencies are folded due to the sample rate of the analog digital converter coinciding with the signal of interest in the passband region of the digital filter. It is therefore desirable to have a method and a system that addresses these problems.